Frequency conversion efficiency

ABSTRACT

According to one embodiment of the invention, improved multipass second harmonic generation (SHG) is provided by the use of an inverting, self-imaging telescope. This embodiment ensures parallelism of all passes of all beams within the nonlinear medium. According to another embodiment of the invention, improved multipass SHG is provided by the use of a wedged phasor. This arrangement provides a simple adjustment of the relative phase of the pump beam and second harmonic beam between passes. According to a further embodiment of the invention, improved multipass SHG is provided by the use of an inverting self-imaging telescope in combination with a wedged phasor. This arrangement provides a simple adjustment of the relative phase of the pump beam and second harmonic beam between passes, and ensures parallelism of all passes of all beams within the nonlinear medium. This arrangement also allows corresponding passes of the pump beam and second harmonic beam to be made collinear within the nonlinear medium. A further embodiment of the invention comprises an OPO having at least one phasor for receiving and adjusting the phase of the one or more beams resonating within the optical cavity which forms part of the OPO. A further OPO embodiment includes first and second telescope assemblies, the optical cavity, phasor and nonlinear medium components of the OPO being situated between the two telescopes.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is a continuation-in-part of application Ser.No. 10/349,379, filed Jan. 21, 2003; the disclosure of which isincorporated by reference.

FIELD OF THE INVENTION

[0002] This invention relates to nonlinear optics, and more specificallyto apparatus and methods for the frequency conversion of laser light.

BACKGROUND OF THE INVENTION

[0003] Existing laser sources do not provide adequate coverage of theentire optical spectrum. Consequently, there has evolved a variety oftechniques for obtaining laser light having a wavelength different fromthat directly emitted by an available laser. Techniques are known todouble the frequency of a laser, to sum or difference the frequency oftwo different lasers to produce a third frequency, or to parametricallygenerate a new frequency. The energy conversion efficiency of mostcommercially available frequency conversion systems is typically lessthan 50%. Thus, it is desirable to provide a technique which willimprove the frequency conversion efficiency of second harmonicgenerators (SHG), sum frequency generators (SFG), difference frequencygenerators (DFG) optical parametric oscillators (OPO), and opticalparametric amplifiers (OPA).

[0004] All of the above-indicated frequency conversion techniques, i.e.,SHG, SFG, DFG, OPO and OPA have, as a common factor, the use of at leastone nonlinear crystal to effect frequency conversion and additionally,all of these embody a three-wave, three-frequency mixing process suchthat the optical frequency of one optical wave equals the sum of theoptical frequencies of the other two optical waves:

ω₁+ω₂=ω₃.

[0005] In addition, for all of the techniques, the change of the opticalpowers obey the Manley-Rowe relations, which describe the conservationof photons,

ΔP ₁/ω₁ =ΔP ₂/ω₂ =−ΔP ₃/ω₃,

[0006] where ΔP_(i) is the change in power of wave, i, caused by thenonlinear conversion process. The techniques differ, however, in whichwaves are input to the nonlinear crystal, and which waves are generatedwithin the nonlinear crystal.

[0007] SFG is the process by which two input waves, at respectivefrequencies ω₁ and ω₂, generate a wave of frequency, ω₃, which is equalto the sum of ω₁ and ω₂. Both inputs are depleted as the sum wave(frequency ω₃) is generated.

[0008] SHG is a degenerate case of SFG in which ω₁=ω₂, so that ω₃=2ω₁.

[0009] DFG is the process by which two input waves, at frequencies ω₃and ω₂, where ω₃>ω₂, generate a wave of frequency ω₁ which is equal toω₃ minus ω₂. As the difference wave at frequency ω₁ is generated, thehigh-frequency input wave, (frequency ω₃₎, is depleted, and the lowerfrequency input wave (frequency ω₂), is amplified. DFG is essentiallythe reverse process of SFG. DFG is often considered to be a relativelylow-efficiency process to distinguish it from OPA, which is described inthe next paragraph. The power of the lower frequency input wave ω₂ isused to generate wave ω₁ at the difference frequency, i.e.,ΔP₁/ω₁<P₂/ω₂, where P₂ is the power of the lower frequency input wavejust prior to the nonlinear conversion.

[0010] OPA is substantially similar to DFG, except in the magnitude ofthe amplification of the low-frequency input wave. The OPA is assumed tohave a high gain, and the amplified low-frequency input wave is used togenerate yet more of the wave at the difference frequency,ΔP₁/ω₁=ΔP₂/ω₂>P₂/ω₂. In practice, either or both of the differenceoutput wave and the amplified low-frequency input wave may be utilized.Generally, the high-frequency input wave is called the “pump wave,” thelow-frequency input wave is called the “signal wave,” and the differenceoutput wave is called the “idler wave.”

[0011] An OPO is an OPA within an optical resonator (resonant opticalcavity), similarly as a laser is an optical gain medium within anoptical resonator. The OPO utilizes the high-frequency input wave likean OPA, but it does not require a low-frequency input wave. In asingly-resonant OPO, the low-frequency wave grows from noise, as lightdoes inside a laser, and circulates (“resonates”) inside the opticalresonator. The same conventions of naming the waves hold as for the OPA.The optical resonator has a set of discrete longitudinal modes for theresonated (“signal”) wave, which determine the discrete frequencies thatthis signal wave may have. The spacing of these frequencies for theresonated signal wave equals the speed of light divided by theround-trip optical path length of the optical resonator for the signalwave. The optical path length is the integral of the refractive indexalong the physical beam path, i.e. nL for a physical length L andrefractive index n. To vary the signal frequency continuously requireschanging the optical path length of the optical resonator as measured atthe signal wavelength. This can be accomplished, for example, bychanging the physical length of the cavity by moving at least one of themirrors of the optical resonator. By increasing the round-trip opticalpath of the resonator by one signal wavelength, the discrete frequenciespermissible to the signal wave are made to decrease by an amount equalto their spacing, without substantially changing their spacing.

[0012] In a doubly-resonant OPO, both of the signal and idler wavesresonate inside the resonant optical cavity, and the frequency of thesignal wave is restricted to the set of discrete frequencies determinedby the optical path of the optical resonator at the signal wavelength,and the frequency of the idler wave is restricted to the set of discretefrequencies determined by the optical path of the optical resonator atthe idler wavelength. Since the sum of the signal and idler wavefrequencies is required to be equal to the frequency of the pump wave,as the signal frequency is increased, the idler frequency will decrease.However, increasing the physical length of the optical resonator willdecrease the permissible discrete frequencies of both signal and idlerwaves. In practice, as the physical length of a doubly-resonant OPOresonator is changed, the signal and idler waves attain significantpower only at those resonator lengths for which a pair of permissiblediscrete signal and idler frequencies exists which sum to the pumpfrequency. These resonator lengths are themselves discrete, thus thesignal and idler wave frequencies cannot be adjusted continuously bythis method. To adjust the signal and idler wave frequenciescontinuously, with a constant pump frequency, requires independentadjustment of the optical path of the resonator at the signal and idlerwavelengths. A pump enhanced doubly-resonant OPO is sometimes referredto as a triply-resonant OPO.

[0013] More generally, for a nonlinear conversion process involving anarbitrary number of waves, the frequency relation is:${{\sum\limits_{i = 1}^{M}{S_{i}\omega_{i}}} = 0},$

[0014] where S_(i)=+1 or −1, i denotes which one of the M beams, andthere is at least one i for which S_(i)=+1 and at least one i for whichS_(i)=−1, and all frequencies ω_(i)≧0. S_(i) is an abstraction toindicate whether the wave i is generated or amplified by the nonlinearmixing process (S_(i)=+1), or depleted by the process (S_(i)=−1). TheManley-Rowe relation is:

S _(i) ΔP _(i)/ω_(i) =S _(j) ΔP _(j)/ω_(j), for all 1≦i, j≦M where jdenotes another beam.

[0015] The special case of SFG is defined by M=3, S₁=S₂=−1, and S₃=+1.

[0016] Examples of 4-wave mixing are Raman scattering, in which,usually, S₁=S₃=+1 and S₂=S₄=−1 and third-harmonic generation (THG) inwhich S₁=S₂=S₃=−1, S₄=+1, and ω₁=ω₂=ω₃.

[0017] Occasionally, it is desirable to cascade nonlinear mixingprocesses. For example, generating the third-harmonic of a frequency ω₁by first SHG of ω₁ and SFG of the resultant second-harmonic ω₃=2ω₁ withthe original ω₁ is sometimes more efficient than direct THG of ω₁. Insuch cases where multiple nonlinear mixing processes exist, each processm is described by its own frequency relation:${\sum\limits_{i = 1}^{M}{S_{m\quad i}\omega_{i}}} = 0.$

[0018] Although, in most descriptions of nonlinear optics, only waveswhich are involved in the mixing process m are included in the equationfor process m, here we include all waves M involved in any of processesm in each such equation, and assign S_(mi)=0 to those waves i notinvolved in mixing process m. Some of the ω_(i) may be shared amongmultiple nonlinear processes, with same or different, non-zero values ofS_(mi) (i.e. +1 or −1) for each process m.

[0019] Increasing either the intensity of the laser source and/orincreasing the nonlinear medium length, or both, can be used to achieveincreased nonlinear conversion efficiency. The intensity can beincreased by using a more powerful pump laser source and/or by focusingthe beam more tightly into the nonlinear medium. There are however,practical limits to how much power a given type of laser source canproduce. Focusing tightly has limited usefulness since diffractioneffects cause the length of the focal region to decrease at the samerate as the intensity increases. Also, for some systems, the damagethreshold intensity for the nonlinear medium is less than the intensityrequired for very high efficiency nonlinear interactions.

[0020] Another technique for increasing conversion efficiency is toincrease the interaction length. In most high power frequency conversiontechniques the nonlinear medium is a birefringent crystal that is cut atan angle such that the pump and generated frequency wave fronts maintainthe phase-matching condition as they copropagate through the crystal.This technique can be applied to systems which are critically,noncritically, or quasi phase matched and can also be used for nonlinearfrequency conversion processes such as frequency up conversion where oneof the sources is a laser and the other source is incoherent radiation.However, the available length of these crystals is limited by thecurrent state of the art of crystal manufacturing and in most cases isless, sometimes considerably less, than a few centimeters. Furthermore,for critical phase matching in birefringent crystals, beams of differentfrequency propagate through the crystal in different directions, aphenomenon referred to as “walk-off”. Walk-off limits the effectiveinteraction length to approximately the beam diameter divided by thewalk-off angle. The efficiency achieved using single-pass nonlinearfrequency conversion such as described in U.S. Pat. Nos. 5,644,584 and6,021,141 is thus limited by crystal length, laser power limitations andwalk-off issues. One known partial solution involves the use of areflective surface to provide for multiple passes through the nonlinearmaterial as described e,g., in U.S. Pat. No. 5,321,718. Alternatively,as described in U.S. Pat. No. 5,500,865, multiple crystals in sequencecan be used. However when focusing is required, such as in the cases ofCW (continuous wave) or CW-mode-locked lasers, the doubling andsum-frequency conversion efficiencies are typically no more than about25%. In the case of most CW lasers, the limiting factors are primarilyshort focal depth and/or inadequate laser intensity. A discussion offrequency conversion theory can be found in “Non-Linear Optics” byRobert W. Boyd, 2^(nd) Edition, 2003 Academic Press, ISBN No.0-12-121682-9, especially pages 4-10 and 79-111, and in “LaserFundamentals” by William Silfvast, Cambridge University Press 1996, ISBNNo. 0-521-55617-1, especially at pages 490-493.

[0021] When effecting multipass frequency conversion, existing frequencyconversion techniques suffer from changes in conversion efficiency dueto changes in the dispersion characteristics of the optical train, whichchanges can arise from a variety of causes. For example, change canoccur due to one or more of the following:

[0022] i) stress induced change in a (the) frequency conversion crystalwhich occurred during assembly.

[0023] ii) change in the alignment of one or more components of theoptical train.

[0024] iii) changes in the composition of the atmosphere in thecontainer housing the optical train.

[0025] iv) changes in the chemistry/structure of the laser gain mediumand/or frequency conversion crystal.

[0026] As described in copending, commonly assigned application Ser. No.10/349,379, it is known to be advantageous to use phasors, either planeparallel or preferably wedged, in an optical train when using amulti-pass or multi-crystal system to effect frequency conversion. Theprimary role of the phasor is to ensure constructive interference amongthe second harmonic beams generated on each pass through the singlecrystal, or each of multiple crystals.

[0027] When dealing with a tunable laser system it is necessary to beable to accommodate a variety of input wavelengths. Also, in some casesit may be advantageous to have means to vary the efficiency of thenon-linear optical conversion.

[0028] Prior art frequency conversion designs also do not provide aconvenient method for detecting and/or correcting the effect of drift inthe laser emission wavelength. It is important to be able to compensatefor these changes so as to maintain the efficiency of the opticalfrequency conversion.

[0029] A common factor in all of the aforementioned frequency conversiontechniques is that, when carried out in accordance with the presentinvention, a phasor will be present in the optical train. Although thepresent invention will be most extensively described in conjunction withsecond harmonic and OPO generation, it is equally applicable to theother aforementioned frequency conversion techniques when a wedged orplane parallel phasor is present in the optical train.

[0030] Second harmonic generation (SHG) is a nonlinear optical processwhere an optical beam, called the pump beam, interacts with an opticallynonlinear medium to generate a second harmonic beam, where the frequencyof the second harmonic beam is twice the frequency of the pump beam.Equivalently, the free space wavelength of the second harmonic beam ishalf the free space wavelength of the pump beam. The pump beam caninteract with the optically nonlinear medium by passing through themedium and/or by being reflected from the medium. In theory, anymaterial which lacks inversion symmetry can be used as the opticallynonlinear medium for SHG. Materials which are suitably used for SHGinclude LiNbO₃, LiTaO₃ and KTiOPO₄ (KTP). For SHG, the non-linearity ofa material is expressed in terms of a second order nonlinearsusceptibility tensor χ⁽²⁾.

[0031] Second harmonic generation (especially when using acontinuous-wave pump beam) tends to be an inefficient process.Efficiency is the ratio of power emitted in the second harmonic beamdivided by the power of the pump beam. The main reason for thisinefficiency is that the nonlinearities provided by optically nonlinearmaterials tend to be weak. Therefore, various measures to improve SHGefficiency have been developed. As indicated, one way to increaseefficiency is to provide more power in the pump beam since the secondharmonic beam power is proportional to the square of the pump beam power(i.e., P_(2ω)<<P_(ω), where P_(2ω) and P_(ω) are the second harmonicpower and pump power, respectively). However, the available pump beampower is usually limited, so methods of increasing SHG efficiency for afixed pump power are of great interest.

[0032] Ensuring phase-matching between the pump beam and the secondharmonic beam is the most important of these methods. Phase-matching iscollinear if the pump and second harmonic wave vectors are parallel, andnon-collinear if the pump and second harmonic wave vectors are notparallel. Collinear phase-matching is generally preferred tonon-collinear phase-matching.

[0033] Assume a pump beam illuminates a section of an opticallynonlinear medium. If the phase-matching condition is not satisfied,second harmonic radiation emitted from various points along theilluminated section will interfere destructively, and as a result, thesecond harmonic beam power will be a periodic function of position, withperiod 2L_(c), along the illuminated section. As taught in U.S. Pat. No.3,407,309 to R. C. Miller, in type I SHG, the coherence length L_(c) isgiven by L_(c)=λ/4Δn, where λ is the free space wavelength of the pumpbeam, Δn=|n_(ω)−n_(2ω)|, where n_(ω) is the refractive index of thenonlinear medium at the pump wavelength and n_(2ω) is the refractiveindex of the nonlinear medium at the second harmonic wavelength. If thephase-matching condition is exactly satisfied, i.e., n_(ω)=n_(2ω), therewill be no destructive interference, and as a result, the secondharmonic beam power will increase monotonically along the illuminatedsection. In a nonlinear device of length L, phase-matching would besufficiently well achieved if L_(c) is comparable to, or larger than, L.Since L is typically on the order of 1 cm, and λ is typically on theorder of 1 μm, Δn must be smaller than about 0.00003 to achievephase-matching in a typical nonlinear optical device.

[0034] Because Δn is typically significantly larger than 0.00003, due tothe dependence of refractive index on wavelength (i.e., dispersion),special methods must be employed to satisfy the phase-matchingcondition. Two of these methods are birefringent phase-matching (BPM)and quasi-phase-matching (QPM). In a birefringent material, the index ofrefraction experienced by an optical beam depends on the polarization ofthe beam. The two states of polarization are called “ordinary” and“extraordinary”, with corresponding indices n_(o) and n_(e), in auniaxial birefringent medium. Type I BPM is accomplished by selecting abirefringent material which emits second harmonic radiation that isorthogonally polarized to the pump radiation and by ensuringn_(oω)≈n_(e2ω)(or n_(eω)≈n_(o2ω)). In other words, the difference inindex due to dispersion is compensated for by the difference in indexdue to polarization, because the pump and second harmonic beams havedifferent states of polarization. In type II BPM, the pump radiationitself is divided between two orthogonal polarizations a and b withinthe nonlinear crystal with refractive indexes n_(ωa) and n_(ωb), and2Δn=|n_(ωa)+n_(ωb)−2n_(2ω)|.

[0035] However, birefringent phase-matching is not always possible. Forexample, a nonlinear material which is not birefringent obviously cannotbe birefringently phase-matched. Even for birefringent materials, it isfrequently desirable for the polarization of the pump and secondharmonic beams to be the same (e.g., to make use of a larger element ofthe χ⁽²⁾ tensor, or to avoid the beam walk-off frequently associatedwith BPM). In these cases, QPM can be employed. As indicated above, in anon-phase-matched interaction, the second harmonic power variesperiodically along an illuminated section of nonlinear material withperiod 2L_(c). Let z be position along the illuminated section. Thesecond harmonic power increases to a maximum in the range 0<z<L_(c) andthen decreases back to zero in the range L_(c)<z<2L_(c), and thisbehavior repeats periodically. Thus the contribution of the secondcoherence length of material to the second harmonic beam exactly cancelsthe contribution of the first coherence length of material to the secondharmonic beam, and the fourth coherence length cancels the thirdcoherence length etc. Basically, the even coherence lengths cancel theodd coherence lengths.

[0036] The purpose of QPM is to disrupt this cancellation byperiodically altering the properties of a nonlinear material so thateach section of length 2L_(c) makes a net contribution to the secondharmonic beam power. This can be accomplished in various ways. Onemethod is to eliminate the non-linearity of every even coherence length(e.g., by selectively disordering the material to set χ⁽²⁾ equal tozero). In this case, the even coherence lengths make no contribution tothe second harmonic beam, and the above cancellation is eliminated.Another method is to periodically change the sign of χ⁽²⁾ so that χ⁽²⁾in all the even coherence lengths is equal, but opposite to, χ⁽²⁾ in allthe odd coherence lengths. This periodic alteration of χ⁽²⁾ can beaccomplished by electrical and/or chemical poling of a ferroelectric orother suitable nonlinear material (e.g., periodic poling of KTiOPO₄), orby epitaxial regrowth techniques for semiconductors (e.g., GaAs). Thesign change of χ⁽²⁾ for the even coherence lengths thus turnsdestructive interference into constructive interference. In other words,the second harmonic emitted by the even coherence lengths addsconstructively to the second harmonic emitted by the odd coherencelengths. Since all parts of the device contribute constructively to theemitted second harmonic when the sign of χ⁽²⁾ is periodically changed,this form of QPM is preferable to QPM obtained by periodically settingχ⁽²⁾ to zero.

[0037] The above (first order) QPM methods require periodic modificationof the properties of a nonlinear material with period 2L_(c). SinceL_(c) is typically small (e.g., Δn=0.01 gives L_(c)=25 μm for λ=1 μm),advanced material fabrication and/or processing technology is typicallyrequired for QPM. QPM can also be accomplished by periodically modifyingmaterial properties with a longer period (e.g., a period of 6L_(c) forthird order QPM, a period of 10L_(c) for fifth order QPM etc.), butthese higher order QPM methods are less efficient than first order QPM.The purpose of higher order QPM is to disrupt the cancellation of an“odd” section of length mL_(c) by the following “even” section of lengthmL_(c), by altering the material properties of each “even” section sothat each section of length 2mL_(c) makes a net contribution to thesecond harmonic beam power. In higher order QPM, m must be odd, so thata section of length mL_(c) makes a nonzero contribution to the secondharmonic beam power.

[0038] The pump beam for SHG generally propagates through a nonlinearmedium as a Gaussian beam which is brought to a focus (i.e., has a beamwaist) inside the nonlinear medium. Phase-matched SHG efficiencyincreases as the pump intensity and interaction length increase, so itis desirable to maximize both of these parameters. However, increasingthe intensity of a beam by bringing it to a smaller focused spotincreases beam divergence, which effectively reduces the interactionlength. Therefore, there is an optimal waist 1/e amplitude radius w forthe pump that maximizes the efficiency of phase-matched SHG in anonlinear medium of length L. The optimal relation (assuming no beamwalkoff between pump and second harmonic) between length L and waistradius w is given by L=L_(opt), where L_(opt)=5.68 πw²n_(ω)/λ, and λ isthe free space pump wavelength. Since SHG efficiency does not have asensitive dependence on L for L near L_(opt), a nonlinear medium lengthL in the range of about L_(opt)/3<L<3 L_(opt) provides nearly optimalperformance. The optimal location of the beam waist within the nonlinearmedium is at the center of the nonlinear medium (i.e., separated fromthe entrance and exit faces by a distance L/2).

[0039] Other methods of increasing SHG efficiency can be employed inaddition to phase-matching and optimal focusing. As indicated, multipassSHG is one such method, where the pump and second harmonic beams makemultiple passes through the nonlinear medium. In multipass SHG, it isnecessary to ensure that the pump and second harmonic beams have theproper relative phase in the second and successive passes, so that thecontribution of each pass to the second harmonic beam is constructive.J. M. Yarborough et al. (Applied Physics Letters 18(3) 1970)demonstrated double pass SHG in birefringently phase-matched LithiumNiobate, where a mirror was used to retro-reflect the pump and secondharmonic beams through the nonlinear medium, and the separation betweenthe mirror and the crystal was varied to control the relative phase ofthe two beams in the second pass via the dispersion of air. G. Imeshevet al. (Optics Letters 23(3) 165, 1998) describe double pass SHG inquasi-phase-matched Lithium Niobate, where a mirror is used toretro-reflect the pump and second harmonic beams through the nonlinearmedium, and the endface of the nonlinear medium facing the mirror ispolished at a small non-zero angle relative to the QPM sectionboundaries. The relative phase of the pump and second harmonic beams inthe second pass is adjusted by translating the nonlinear medium withrespect to the beams to vary the medium thickness seen by the beams.

[0040] Translating a mirror to control the relative phase of the pumpand second harmonic beams on the second pass has the disadvantage that asignificant range of motion is required (e.g., on the order of severalcm). Translating a wedged nonlinear optical medium to control therelative phase of the pump and second harmonic beams on the second passis undesirable, because temperature control of the nonlinear medium istypically required, which complicates the design, and the size of thenonlinear medium must be increased to accommodate the translation.Retro-reflection of the pump beam does not preserve optimal focusing ofthe pump beam from the first pass to the second pass. In other words, ifthe pump beam is optimally focused for a first pass through a nonlinearmedium, and a second pass is obtained by retro-reflection, the secondpass pump beam will not be optimally focused through the nonlinearmedium.

[0041] One object of the present invention is to provide an improvedapparatus and method which provides a tunable/adjustable phasor betweenco-propagating, although not necessarily collinear, optical waves ofdifferent wavelengths. In particular, it is an object of the presentinvention to provide an apparatus and method which permits theadjustment of a phasor (i.e., changing its refractive index), present inthe optical train subsequent to the initial assembly and throughout theservice life of the frequency conversion apparatus.

[0042] A preferred embodiment is a method and apparatus to adjust therelative phase of the pump beam and second harmonic beam in multipassSHG.

[0043] A further object of the present invention is to provide animproved apparatus and method for adjusting the relative phase among allof the waves in a multipass nonlinear conversion process.

[0044] A further object of the present invention is to provide animproved apparatus and method for adjusting the relative phase among allof the waves in each of multiple, simultaneous multipass nonlinearconversion processes.

[0045] Another object of the invention is to provide an apparatus andmethod for ensuring that each beam on each pass is parallel to that beamon all other passes. For multipass SHG, this apparatus and methodensures that the pump beam on each pass is parallel to the pump beam onall other passes, and that the second-harmonic beam on each pass isparallel to the second-harmonic beam on all other passes.

[0046] Yet another object of the invention is to preserve optimalfocusing of each beam for all passes.

[0047] A further object of the invention is to provide an apparatus andmethod for ensuring that the second-harmonic beam generated on each passis collinear with the second-harmonic beams generated on all successivepasses. That is, making a second harmonic beam generated on the firstpass of the pump beam through the nonlinear medium collinear with thesecond harmonic beam generated on the second and all subsequent passesof the pump beam.

[0048] Another object of the invention is to provide an improvedapparatus and method for continuous tuning of the signal frequency of asingly resonant OPO.

[0049] Yet another object of the invention is to provide an apparatusand method for continuous tuning of the signal and idler frequencies ofa doubly resonant OPO.

[0050] Another object of the invention is to provide an apparatus andmethod for continuous tuning of the signal and idler frequencies of apump-enhanced singly or doubly resonant OPO, with a fixed or tunablepump frequency. In such OPOs, the pump wave resonates in the opticalresonator in addition to the signal wave, or signal and idler waves.

DESCRIPTION OF THE INVENTION

[0051] A phasor is a dispersive optical element, i.e., the refractiveindex is a non-constant function of the wavelength; thus, the opticalphase accumulated upon transmission is not substantially proportional tothe optical frequency. The ability to tune or adjust the difference inoptical phase after the phasor has been placed in the optical train hasseveral advantages, including:

[0052] a) To fine-tune the phase difference or compensate for stressesin the frequency conversion crystal acquired during optical assembly.

[0053] b) To compensate for changes in the dispersion of components inthe optical train over time (including the gas between solid opticalcomponents), or changes in the alignment of optical components overtime.

[0054] c) To accommodate a variety of wavelength combinations, such asfor tunable SHG.

[0055] d) To vary the net efficiency of non-linear optical conversion ina multi-pass scheme by causing the relative optical phase on successivepasses to be at a controllable value. In the case of SHG this determineswhether second harmonic beams generated on each pass interfereconstructively or destructively and to what extent.

[0056] According to one embodiment of the present invention, improvedmultipass SHG is provided by the use of at least one adjustable phasor,preferably a wedged phasor. This arrangement enables adjustment of therelative phase of the interacting optical waves, i.e., the pump beam andsecond harmonic beam between passes.

[0057] According to one preferred embodiment of the invention, improvedmultipass SHG is provided by the use of an inverting self-imagingtelescope in combination with a wedged phasor as described inco-pending, commonly assigned U.S. patent application Ser. No.10/349,379 filed Jan. 21, 2003, the entire disclosure of which isincorporated herein by this reference. This arrangement provides asimple adjustment of the relative phase of the pump beam and secondharmonic beam between passes, and ensures parallelism of all passes ofall beams within the nonlinear medium. This arrangement allows thesecond harmonic beam generated on each pass to be made collinear uponsubsequent passes within the nonlinear medium with the second harmonicbeam generated on those subsequent passes.

[0058] Numerous methods can be used to effect the dispersion of thephasor by changing its refractive index, including:

[0059] 1) Thermo-optic tuning.

[0060] 2) Electro-optic tuning.

[0061] 3) Elasto-optic tuning.

[0062] The particular geometry of the phasor (e.g., wedge, angle ofincidence) and its location within the optical train (e.g., phasoroutside or within the telescope, choice of full telescope or singleconcave or planar mirror) do not affect the tunability of the phasor.The refractive index at each of the relevant wavelengths should changeso that the net optical phase difference also changes.

[0063] This phase difference Δφ for a combination of three waves is:${{\Delta\varphi} = {2\pi \quad {L( {\frac{n_{3}}{\lambda_{3}} - \frac{n_{2}}{\lambda_{2}} - \frac{n_{1}}{\lambda_{1}}} )}}},$

[0064] where n_(i) is the refractive index of wave i including theeffect of the polarization of wave i, λ_(i)=c/ω_(i) is the free-spacewavelength of wave i, c is the free space velocity of light, and L isthe path length of the optical beam through the phasor. This definitionof the phase difference is relevant for a combination of waves, thefrequencies of which obey,

ω₁+ω₂=ω₃,

[0065] as described in the background of the invention. The tuningmethod, the particular phasor material, and/or the length of the phasormay be chosen to optimize the tuning rate for a given application.

[0066] For the special case of type I SHG, for which ω₁=ω₂ andfundamental waves 1 and 2 have the same polarization, the phasedifference is:${{\Delta\varphi} = {2\pi \quad {L( {\frac{n_{3}}{\lambda_{3}} - \frac{2n_{1}}{\lambda_{1}}} )}}},$

[0067] where wave 3 is the second harmonic wave. For type II SHG, thetwo fundamental waves have different polarizations, and hence, couldhave different refractive indexes in the phasor if the phasor isbirefringent. Therefore, for type II SHG with a birefringent phasor, theequation of the phase difference for a combination of three wavesapplies, with λ₁=λ₂, but with separate n₁ and n₂.

[0068] More generally, for an arbitrary number of waves, the phasedifference is:${{\Delta\varphi} = {2\pi \quad L{\sum\limits_{i = 1}^{M}\frac{S_{i}n_{i}}{\lambda_{i}}}}},$

[0069] which is relevant for a combination of waves, the frequencies ofwhich obey: ${{\sum\limits_{i = 1}^{M}{S_{i}\omega_{i}}} = 0},$

[0070] As indicated, for type I second harmonic generation, this phasedifference is:${\Delta\varphi} = {2\pi \quad {L( {\frac{n_{SH}}{\lambda_{SH}} - \frac{2n_{f}}{\lambda_{f}}} )}}$

[0071] where n_(SH) is the refractive index of the second-harmonic beam,λ_(SH) is the free-space wavelength of the second-harmonic beam, n_(f)is the refractive index of the fundamental beam, λ_(f) is the free-spacewavelength of the fundamental beam and L is the path length of theoptical beam through the phasor. The tuning method, the type of phasormaterial, and/or the length of the phasor may be chosen to optimize thetuning rate for a given application.

[0072] As a first example, consider a glass phasor. This is most easilytuned using temperature (thermo-optic) tuning e.g., with a Peltier unitin contact with the phasor. To obtain a change in phase difference of 2πbetween a 976 nm fundamental wave and 488 nm second-harmonic waverequires approximately 3° C. of temperature range for a 5 mm long phasorof SF6 glass, double-passed.

[0073] As a second example, consider a 12 mm. long KTP phasor. This canbe tuned by temperature over a few degrees C. It can be tuned by theelectro-optic effect (having relatively large electro-optic coefficientsfor tuning/polarization axis combinations) by applying an electric fieldto the KTP. It can also be tuned by the elasto-optic effect by applyinga mechanical strain (such as compression) to the KTP.

[0074] According to another embodiment of the invention, an improved setof multiple simultaneous multipass nonlinear mixing processes isprovided by the use of plural adjustable phasors, preferably wedgedphasors. The suitable number of phasors equals the number ofsimultaneous multipass nonlinear mixing processes. Each phasor has adifferent dispersion, so that the changes in the optical path lengths ofthe optical waves by adjustment of the set of phasors is linearlyindependent: any combination of relative phases of all simultaneousnonlinear processes can be achieved by adjustment of the phasors. Therelative phase of process m is described by:${{\Delta\varphi}_{m} = {2\pi \quad L{\sum\limits_{i = 1}^{M}\frac{S_{m\quad i}n_{i}}{\lambda_{i}}}}},$

[0075] where M, and S_(mi) are as defined above for multiple nonlinearprocesses, and which is relevant for a combination of waves, thefrequencies of which obey:${{\sum\limits_{i = 1}^{M}{S_{m\quad i}\omega_{i}}} = 0},$

[0076] According to a further embodiment of the invention, an improvedset of multiple simultaneous multipass nonlinear mixing processes isprovided by the use of an inverting self-imaging telescope preferably incombination with multiple wedged phasors.

[0077] According to a further embodiment of the invention, an improvedcontinuously tunable singly-resonant OPO is provided by the use of anadjustable phasor, preferably a wedged phasor. Adjustment of this phasorpermits continuous tuning of the resonating signal beam frequency, whichthereby results in continuous tuning of the idler frequency.

[0078] According to a further embodiment of the invention, an improvedcontinuously tunable pump-enhanced singly-resonant OPO is provided bythe use of an adjustable phasor, preferably a wedged phasor. Adjustmentof this phasor, if desired in conjunction with adjustment of thephysical length of the OPO optical resonator, and/or an additionalphasor, permits continuous tuning of the resonating signal frequencywhile the pump frequency remains constant and resonant in the OPO, whichthereby results in continuous tuning of the idler frequency.Alternatively, the pump frequency may also be tuned, and the adjustmentof phasors and/or cavity length performed such that the pump frequencyremains resonant in the OPO and such that the signal frequency is tuned.

[0079] According to yet another embodiment of the invention, an improveddoubly-resonant OPO is provided by the use of an adjustable phasor,preferably a wedged phasor. Adjustment of this phasor, optionally incombination with adjustment of the physical length of the OPO opticalresonator, and/or an additional phasor, permits continuous tuning of thesignal and idler frequencies while the pump frequency remains constant.Use of a wedged phasor of only one optical material to effect continuoustuning requires simultaneous adjustment of the physical opticalresonator length. Use of a phasor consisting of two wedges of opticalmaterials of different optical dispersion can eliminate the need forsimultaneous adjustment of the physical optical resonator length, byappropriate choice of the optical materials (optical dispersion) andwedge angles. Alternatively, two wedges of optical materials ofdifferent optical dispersion adjusted simultaneously also effectscontinuous frequency tuning.

[0080] According to yet another embodiment of the invention, an improvedpump-enhanced doubly-resonant OPO is provided by the use of one or twoadjustable phasors, preferably wedged phasors. Adjustment of one or twophasors, optionally in combination with adjustment of the physicallength of the OPO optical resonator, and/or a third phasor, permitscontinuous tuning of the signal and idler frequencies while the pumpfrequency remains constant and resonant in the OPO. Use of only twowedged phasors, each of only one optical material, to effect continuoustuning requires simultaneous adjustment of the physical opticalresonator length. Use of a phasor consisting of two wedges of opticalmaterials of different optical dispersion can eliminate the need forsimultaneous adjustment of the optical resonator length or for a thirdphasor, by appropriate choice of the optical materials (i.e., opticaldispersion) and wedge angles. Alternatively, two wedges of opticalmaterials of different optical dispersion adjusted simultaneously may beequivalent to a phasor consisting of two wedges. Use of a phasorconsisting of three wedges of optical materials of different opticaldispersion can eliminate the need for simultaneous adjustment of thephysical optical resonator length or of any other phasor, by appropriatechoice of the optical materials (i.e., optical dispersion) and wedgeangles. Alternatively, three wedges of optical materials of differentoptical dispersion adjusted simultaneously may be equivalent to a phasorconsisting of three wedges.

BRIEF DESCRIPTION OF THE DRAWINGS

[0081]FIG. 1a is a schematic top view of a double pass SHG embodiment ofthe invention.

[0082]FIG. 1b is a schematic end view of a nonlinear medium in a doublepass SHG embodiment of the invention.

[0083]FIG. 2a is a schematic top view of a quadruple pass SHG embodimentof the invention.

[0084]FIG. 2b is a schematic end view of a nonlinear medium in aquadruple pass SHG embodiment of the invention.

[0085]FIG. 3 is a schematic top view of a double pass embodiment of theinvention applied to two simultaneous nonlinear mixing processes.

[0086]FIG. 4 is a schematic top view of a singly-resonant OPO embodimentof the invention.

[0087]FIG. 5a is a schematic top view of a doubly-resonant OPOembodiment of the invention using only one phasor of one material.

[0088]FIG. 5b is a schematic top view of a doubly-resonant OPOembodiment of the invention using two phasors of different materials(different dispersions).

[0089]FIG. 5c is a schematic top view of a doubly-resonant OPOembodiment of the invention using one phasor composed of two wedges ofdifferent materials (different dispersions).

[0090]FIG. 6 is a schematic top view of a pump-enhanced doubly-resonantOPO (sometimes called a triply-resonant OPO) embodiment of the inventionusing one phasor composed of three wedges of different materials(different dispersions).

DETAILED DESCRIPTION OF THE DRAWINGS

[0091]FIG. 1a is a schematic top view of a double pass frequencydoubling apparatus 40, in accordance with the present invention, whileFIG. 1b is a schematic end view of a nonlinear medium 10 withinapparatus 40. To appreciate the operation of apparatus 40, it is helpfulto consider the beam paths through apparatus 40 before discussing thedesign of apparatus 40 in detail. A pump beam provided by a pump source42 is received by a face 10-2 of nonlinear medium 10, and is transmittedalong a beam path 30 through nonlinear medium 10. A second harmonicbeam, with frequency twice the pump frequency, is generated withinnonlinear medium 10, and is also transmitted along beam path 30 throughnonlinear medium 10. The pump and second harmonic beams are emitted froma face 10-1 of nonlinear medium 10, and are received by a phasor 16. Thebeams are transmitted through phasor 16 and are received by a mirror 18.The pump and second harmonic beams are then reflected by mirror 18 andare received by a mirror 20. Both beams are reflected by mirror 20,reflected again from mirror 18, transmitted again through phasor 16, andreceived by face 10-1 of nonlinear medium 10. The second pass pump andsecond harmonic beams are transmitted along a beam path 32 throughnonlinear medium 10, and are emitted from face 10-2 of nonlinear medium10.

[0092] Beam paths 30 and 32 through nonlinear medium 10 are preferablyparallel to and spaced apart from each other, as indicated on FIG. 1b.This is accomplished by choosing mirrors 18 and 20 such that they act asan inverting telescope to re-image a reference plane 12 located at thecenter of nonlinear medium 10 onto itself with negative unitymagnification. Axis 14 is the axis of the telescope formed by mirrors 18and 20, and is substantially centered within nonlinear medium 10 asindicated in FIGS. 1a and 1 b. Thus, beam path 32 is the image of beampath 30 formed by the inverting telescope, and separation of beam paths30 and 32 is obtained by offsetting beam path 30 from axis 14 asindicated in FIG. 1b. This separation of the second pass (beam path 32)from the first pass (beam path 30) is advantageous, since no additionaloptical elements are required to separate the second pass beams from thefirst pass beams.

[0093] Nonlinear medium 10 can be any material which lacks inversionsymmetry. Preferably, nonlinear medium 10 is phase-matched to increaseSHG efficiency. Periodically-poled KTP (KTiOPO₄) is one suitablenonlinear medium 10, but other nonlinear materials, such as LithiumNiobate, Lithium Tantalate, or beta-Barium Borate, can also be used topractice the invention, using phase-matching techniques, including butnot limited to, birefringent phase-matching and quasi-phase-matching. Insome cases, it is important to avoid reflection of the pump beam backinto the pump source; and in these cases, nonlinear medium 10 (or face10-2 of nonlinear medium 10) can be slightly tilted (by approximately 1degree to a few degrees) so that the pump beam is not exactly normallyincident on face 10-2 of nonlinear medium 10. This ensures that the pumpbeam reflected from face 10-2 of nonlinear medium 10 does not coupleback into the pump source. Preferably, faces 10-1 and 10-2 of nonlinearmedium 10 are anti-reflection coated to provide a low reflectivity (i.e.reflectivity <1 percent, more preferably <0.5 percent) at both the pumpfrequency (or wavelength) and second harmonic frequency (or wavelength)to reduce loss in apparatus 40.

[0094] The purpose of phasor 16 is to adjust the relative phase of thepump and second harmonic beams as the beams enter nonlinear medium 10for a second or subsequent pass (i.e., beam path 32) so that the secondpass contributes constructively to the second harmonic beam alreadypresent from the first pass. Phasor 16 is fabricated as a wedged plateof a dispersive optical material, i.e., a material which has a differentindex of refraction at the pump frequency and second harmonic frequency,where the wedge angle between the phasor surfaces is roughly on theorder of 0.1 degree to 1 degree. Because phasor 16 is a wedged plate,the amount of dispersive material it introduces into the beam path isvariable by translating the phasor perpendicular to the beams. Forexample, consider doubling of 976-nm radiation to 488 nm. A suitablematerial for phasor 16 is the commercial glass BK7, which hasn_(ω)=1.508 and n_(2ω)=1.522 at these wavelengths, respectively. Thecoherence length of BK7 in this example is L_(c)=17.4 μm. Since the beammakes a double pass through phasor 16, a full 2π adjustment of therelative phases of pump and second harmonic beams is obtained by varyingthe phasor thickness seen by the beams by L_(c)=17.4 μm. Phasor 16 ispreferably inserted into assembly 40 so that both pump and secondharmonic beams are incident on phasor 16 at or near Brewster's angle andhave p polarization (i.e., electric field vector lying in the plane ofincidence of a phasor surface), to reduce reflection losses from thesurfaces of phasor 16. Alternatively, phasor 16 may have anantireflection coating on its optical surfaces so that the phasor can beused at angles other than Brewster's angle without introducingsubstantial reflection losses.

[0095] Mirror 18 is a concave mirror with a radius of curvature R.Mirror 20 is a flat mirror which is separated from mirror 18 by a lengthL which is substantially equal to the focal length f=R/2 of mirror 18.Mirrors 18 and 20 are highly reflective (with a reflectivity preferablygreater than 99.5 percent) at both the pump and second harmonicfrequencies. Mirrors 18 and 20 together form a telescope subassemblyhaving an ABCD matrix (for both the pump and second harmonic beams) withA=−1, B has a real value which depends on the location of plane 11relative to mirror 18, C=0 and D=−1, with respect to an input and outputreference plane 11 located between mirror 18 and phasor 16. The ABCDmatrix describes the geometrical imaging properties of an optical systemas follows: $\begin{matrix}{\begin{pmatrix}y \\y^{\prime}\end{pmatrix} = {\begin{pmatrix}A & B \\C & D\end{pmatrix}\begin{pmatrix}x \\x^{\prime}\end{pmatrix}}} & (1)\end{matrix}$

[0096] where x and x′ are the position and slope, respectively, of aninput ray relative to the optical axis of the system (i.e., axis 14 onFIG. 1a) at the input reference plane of the optical system, and y andy′ are the position and slope, respectively, of the corresponding outputray at the output reference plane of the optical system.

[0097] Any basic optical element can be expressed with a single ABCDmatrix. For example, a propagation distance L through medium with indexof refraction n can be expressed with the following ABCD matrix:$\begin{bmatrix}1 & {L/n} \\0 & 1\end{bmatrix}\quad$

[0098] Similarly, a simple thin lens is expressed with the followingABCD matrix: $\begin{bmatrix}1 & 0 \\{{- 1}/f} & 1\end{bmatrix}.$

[0099] The ABCD matrices for more complicated multi-element systems canbe obtained by matrix multiplication of the cascaded basic elements. Forexample, consider the inverting telescope used in Applicants' inventionto redirect the beams between passes in the multipass geometry. Thistelescope consists physically of two elements: concave mirror 18 andplano mirror 20. In matrix formalism, and replacing the concave mirrorwith the functionally equivalent thin lens of focal length R/2, thistelescope consists of three ABCD matrix elements: a thin lens (theconcave mirror), a free space distance equal to twice the separation ofelements 18 and 20, and a second identical thin lens (the secondreflection off the concave mirror). The ABCD matrix representing thisassemblage is the product of the three matrices for the above elements,or: ${\begin{bmatrix}1 & 0 \\{{- 1}/f} & 1\end{bmatrix}\begin{bmatrix}1 & {L/n} \\0 & 1\end{bmatrix}}\begin{bmatrix}1 & 0 \\{{- 1}/f} & 1\end{bmatrix}$

[0100] If we set the separation of the two elements 18 and 20 to beequal to the focal length f, then the distance L/n=2f. If one thenperforms the matrix multiplication the following result is obtained:$\begin{matrix}{= {\begin{bmatrix}1 & 0 \\{{- 1}/f} & 1\end{bmatrix}\begin{bmatrix}{- 1} & {2f} \\{{- 1}/f} & 1\end{bmatrix}}} \\{= \begin{bmatrix}{- 1} & {2f} \\0 & {- 1}\end{bmatrix}}\end{matrix}$

[0101] We thus see that the ABCD matrix for the −1 magnificationtelescope has A=D=−1, and C=0. In this single lens telescope, the valuefor B=2ƒ; perforce a real number. For a given off-axis angular alignmentof a beam input into the telescope, B represents the relationshipbetween a given off-axis angular alignment of a beam input to thetelescope and the resulting positional output alignment. Thus, any realvalue for B will bring equivalent benefits from use of the telescope.

[0102] For optical systems which retro-reflect a beam, it is frequentlyconvenient to select the same plane (e.g., reference plane 11) as theinput reference plane and as the output reference plane.

[0103] Mirror 18 is preferably positioned such that the diffractivedistance between reference plane 12 at the center of nonlinear medium 10and mirror 18 is substantially equal to the focal length of mirror 18.The diffractive distance between two points separated by regions oflength L_(i) and index n_(i) is, in most instances, ΣL_(i)/n_(i). Thecomputation of the refractive distance is more complex for birefringentmedia, such as nonlinear crystals. With this relative positioning ofmirror 18 and nonlinear medium 10, reference plane 12 is re-imaged ontoitself (with −1 magnification, i.e., inversion) by the telescopesubassembly. This ensures that optimal focusing is preserved from onepass to the next. That is, if the first pass pump beam is optimallyfocused through nonlinear medium 10, (i.e., it has a beam waist of theappropriate size at reference plane 12 at the center of nonlinear medium10), the second pass pump beam will also be optimally focused throughnonlinear medium 10.

[0104] Although the primary purpose of the telescope subassembly is tocouple the pump and second harmonic beams emitted from nonlinear medium10 after the first pass back into nonlinear medium 10 for a second pass,the above properties of the ABCD matrix of the telescope subassemblyhave additional advantageous consequences.

[0105] The condition C=0 ensures that the output ray slope depends onlyon the input ray slope (i.e., it does not depend on input ray position).Therefore, two rays which are parallel at the input of an optical systemwith C=0 will be parallel at the output of that system. Optical systemswith C=0 are telescopes. The condition D=−1, in combination with thecondition C=0, ensures that the first pass and second pass ray slopes ofthe pump beam (and the first pass and second pass ray slopes of thesecond harmonic beam) are identical between phasor 16 and mirror 18. Thesign change of the ray slope from D=−1 is cancelled out by the signchange due to the reversal of the optical axis. This equality of rayslopes also extends into nonlinear medium 10, since there are nofocusing elements between mirror 18 and nonlinear medium 10, so thesecond pass pump beam is parallel to the first pass pump beam withinnonlinear medium 10, and the second pass second harmonic beam isparallel to the first pass second harmonic beam within nonlinear medium10. Parallelism between first and second passes is advantageous becausephase-matching typically has a narrow angular acceptance. If the firstand second passes go through nonlinear medium 10 at significantlydifferent angles, it may be impossible to efficiently phase-match bothpasses simultaneously.

[0106] The preservation of beam parallelism between the first and secondpasses also ensures that the linearly varying thickness of phasor 16across the beam cross-sections is cancelled in a double pass throughphasor 16. In other words, the relative phase shift imparted to thesecond harmonic beam relative to the pump beam by a double pass throughphasor 16 does not vary from point to point within the beams. Similarly,if nonlinear medium 10 has a linearly varying thickness from point topoint within the beams (e.g. if face 10-1 is tilted with respect to thebeams and face 10-2 is not tilted), the effect on relative optical phasedue to this variable thickness is cancelled in a double pass.

[0107] The arrangement of mirror 18 and mirror 20 shown in FIG. 1a is apreferred telescope subassembly, since mirror 18 has the same focallength at both the pump and second harmonic frequencies. Other telescopesubassemblies with A=−1, C=0 and D=−1 (at both pump and second harmonicwavelengths) are also suitable for practicing the invention. In allcases it is preferred to position the telescope subassembly relative tononlinear medium 10 such that reference plane 12 at the center ofnonlinear medium 10 is substantially re-imaged onto itself with −1magnification, in order to preserve optimal focusing from one pass tothe next, i.e. B=0

[0108] Although the telescope subassembly with A=−1, C=0 and D=−1ensures beam parallelism within nonlinear medium 10, beam collinearityof the second-harmonic generated on the first pass with that generatedon the second pass within nonlinear medium 10 is not ensured by thetelescope subassembly. In other words, it is possible for the axis inthe second pass of the second harmonic beam generated on the first passto be laterally separated from the axis of the second harmonic beamgenerated on the second pass. This is because in the second pass, thesecond harmonic generated on the first pass may be displaced from thefundamental differently from in the first pass. Two sources of thisundesirable beam offset are the dispersion of phasor 16 and thedispersion of nonlinear medium 10 (if the beams intersect face 10-1 ofnonlinear medium 10 at a non-normal angle of incidence). The beam offsetis affected by the wedge angle of phasor 16, the nominal thickness ofphasor 16, the angle of incidence on the phasor, the length of nonlinearmedium 10 (assuming the design is constrained to re-image referenceplane 12 onto itself with −1 magnification), the angle of incidence onface 10-1 of nonlinear medium 10, and the distance between phasor 16 andnonlinear medium 10. Since varying these parameters changes the beamoffset without affecting the parallelism preserving property of thetelescope subassembly (i.e. the relative angle between fundamental andsecond harmonic beams), the beam offset can be eliminated by design.

[0109] An additional consideration in a detailed design is astigmatismcompensation, because phasor 16 and mirror 18 both cause astigmatism.The relevant parameters are the thickness, incidence angle and wedgeangle of phasor 16, and the focal length and incidence angle of mirror18. Again, these parameters offer enough flexibility to eliminate thenet astigmatism of apparatus 40 by design (i.e., by ensuring that theastigmatism of phasor 16 compensates for the astigmatism of mirror 18,and conversely). In addition, there are enough parameters to eliminateastigmatism and to preserve collinearity simultaneously. It is desirableto ensure that apparatus 40 has no net astigmatism, to maximizeconversion efficiency and to provide a non-astigmatic second harmonicbeam after the second pass. It is also possible to eliminate astigmatismfrom apparatus 40 by adding one or more optical elements to apparatus 40in accordance with known principles of telescope astigmatismcompensation.

[0110] To generalize to a double-pass, nonlinear optical frequencymixing apparatus with an arbitrary number of waves in a singlephase-matched process as described by a single sum of frequencies, onecan substitute “input beam” for “pump beam” and substitute “additionalbeams” for “second harmonic beam” in the foregoing description of theembodiment shown in FIG. 1. Input waves can be either amplified ordepleted, while additional waves are always amplified. Waves designatedi are only input waves such that S_(i)=−1, while waves designated j canbe either input waves or additional waves such that S_(j)=+1. Allresults described for FIG. 1 are still valid except that because in theembodiment of FIG. 1 there is only a single input beam i there can be nooverlap of waves i. Also, to achieve the collinearity of each wave jgenerated on all passes, plural phasors may be required. The waves jgenerated on each pass can be made collinear for at least one j bydesigning the optical system as described above for FIG. 1 by selectingan appropriate phasor shape, although there must be sufficient degreesof freedom to obtain this collinearity for more than one j.Alternatively, the location of the intersection (or collinearity) of twobeams i₁ and i₂ may be maintained among all passes by design, althoughagain there must be sufficient degrees of freedom to obtain thisproperty for more than one pair of beams. The use of additional phasorscan provide enough degrees of freedom to obtain optimum intersection ofall beams i and the collinearity of the beams of each j generated oneach pass.

[0111]FIG. 2a is a schematic top view of a four pass frequency doublingapparatus 50, in accordance with the present invention, while FIG. 2b isa schematic end view of nonlinear medium 10 within apparatus 50. Toappreciate the operation of apparatus 50, it is helpful to consider thebeam paths through apparatus 50 before considering the design ofapparatus 50 in detail. A pump beam is received by face 10-2 ofnonlinear medium 10, and is transmitted along beam path 30 throughnonlinear medium 10. A second harmonic beam, with a frequency twice thepump frequency, is generated within nonlinear medium 10, and is alsotransmitted along beam path 30 through nonlinear medium 10. The pump andsecond harmonic beams are emitted from face 10-1 of nonlinear medium 10,and are received by phasor 16. The beams are transmitted through phasor16 and are received by mirror 18. The pump and second harmonic beams arereflected by mirror 18 and are received by mirror 20. Both beams arereflected by mirror 20, reflected again from mirror 18, transmittedagain through phasor 16, and received by face 10-1 of nonlinear medium10. The pump and second harmonic beams are transmitted in a second passalong beam path 32 through nonlinear medium 10, and are emitted fromface 10-2 of nonlinear medium 10.

[0112] These two emitted beams are received by a phasor 16′, transmittedthrough phasor 16′, received by a mirror 18′, reflected from mirror 18′and received by a mirror 20′. After reflection from mirror 20′, the pumpand second harmonic beams are reflected again from mirror 18′,transmitted again through phasor 16′, and received by face 10-2 ofnonlinear medium 10. The pump and second harmonic beam are transmittedin a third pass along beam path 34 through nonlinear medium 10, and areemitted from face 10-1 of nonlinear medium 10.

[0113] These two emitted beams are received by phasor 16, transmittedthrough phasor 16, received by mirror 18, reflected from mirror 18, andreceived by mirror 20. After reflection from mirror 20, the pump andsecond harmonic beams are reflected again from mirror 18, transmittedagain through phasor 16, and received by face 10-1 of nonlinear medium10. The pump and second harmonic beams are transmitted in a fourth passalong beam path 36 through nonlinear medium 10, and are emitted fromface 10-2 of nonlinear medium 10.

[0114] Beam paths 30, 32, 34 and 36 through nonlinear medium 10 areseparated from each other, as indicated on FIG. 2b. This is accomplishedby choosing mirrors 18 and 20 such that they act as a first invertingtelescope to re-image reference plane 12 located at the center ofnonlinear medium 10 onto itself with negative unity magnification. Axis14, which is the axis of the telescope formed by mirrors 18 and 20, issubstantially centered within nonlinear medium 10 as indicated on FIG.2b . Thus, beam path 32 is the image of beam path 30 formed by theinverting telescope, and separation of beam paths 30 and 32 is obtainedby offsetting beam path 30 from axis 14 as indicated on FIG. 2b. Mirrors18′ and 20′ are also selected such that they act as an invertingtelescope to re-image reference plane 12 onto itself with negative unitymagnification. Axis 14′ is the axis of the second telescope formed bymirrors 18′ and 20′, and is offset from axis 14 as indicated on FIG. 2b.Thus, third pass beam path 34 is the image of second pass beam path 32formed by this second inverting telescope. Similarly, fourth pass beampath 36 is the image of third pass beam path 34 formed by the firstinverting telescope with axis 14. Therefore, all four passes followdistinct paths through nonlinear medium 10, where second pass beam path32 is the inversion of first pass beam path 30 about axis 14, third passbeam path 34 is the inversion of second pass beam path 32 about axis14′, and fourth pass beam path 36 is the inversion of third pass beampath 34 about axis 14.

[0115] Since the four passes in apparatus 50 do not overlap, no beamsplitters (which introduce undesirable loss) are required to couple thepump beam into apparatus 50, or to couple the second harmonic beam outof apparatus 50. A preferred method for coupling the pump beam intoapparatus 50 is to position a pump turning mirror 46 within apparatus 50so that a pump beam provided by pump source 42 is reflected to followbeam path 30 through nonlinear medium 10, and such that pump turningmirror 46 does not block the second pass beams following beam path 32through nonlinear medium 10 or the third pass beams following beam path34 through nonlinear medium 10.

[0116] A preferred method for coupling the second harmonic beam out ofapparatus 50 is to position a second harmonic turning mirror 44 withinapparatus 50 so that the fourth pass second harmonic beam following beampath 36 through nonlinear medium 10 is reflected out of apparatus 50,and such that second harmonic turning mirror 44 does not block the firstpass pump beam following beam path 30 through nonlinear medium 10, thesecond pass beams following beam path 32 through nonlinear medium 10, orthe third pass beams following beam path 34 through nonlinear medium 10.

[0117] Phasor 16′ has the same characteristics as phasor 16 in FIG. 1a.The first and second telescopes in apparatus 50 (formed by mirrors 18and 20, and by mirrors 18′ and 20′, respectively) are both designed asindicated in the discussion of FIG. 1a, i.e., with A=D=−1 and C=0 at therelevant phasor (i.e., phasor 16 for the telescope formed by mirrors 18and 20, and phasor 16′ for the telescope formed by mirrors 18′ and 20′),and designed to re-image reference plane 12 onto itself with −1magnification. This arrangement provides the advantages of beamparallelism on all four passes, and beam collinearity and astigmatismcompensation by design, also as indicated above. In addition, phasor 16applies the same relative phase shift between the first and secondpasses of the beams as it does between the third and fourth passes ofthe beams. Because the beam pattern for the four passes is highlysymmetrical, the required phase shift between the first and secondpasses and between the third and fourth passes is the same. Therefore,phasor 16 can simultaneously provide the required phase shift betweenthe first and second passes, as well as between the third and fourthpasses, which is highly desirable compared to an alternative where threeindependent phasors are used in four pass SHG. Even if a linearlyvarying phase shift is imposed on the beams by nonlinear medium 10 (e.g.if face 10-1 is not exactly perpendicular to the beam axes), thisvariation is cancelled in double pass, and phasor 16 will stillsimultaneously provide the required phase shift between the first andsecond passes, as well as between the third and fourth passes.

[0118] In many instances it is correct to make the assumption that thepump beam and second harmonic beam are collinear within nonlinear medium10 on the first pass. This assumption is for collinear QPM or collinearBPM with negligible beam walkoff. In some cases, such as birefringentphase-matching with nonzero beam walkoff, the pump and second harmonicbeams are not collinear over the entire length of nonlinear medium 10.In other cases, such as non-collinear phase-matching, the pump andsecond harmonic beams are not parallel within nonlinear medium 10. Forthese cases, the apparatus and methods discussed above are alsoadvantageous, since compensation methods analogous to the lateral offsetcompensation discussed above can be applied to ensure that the secondpass “undoes” the divergence of the pump beam from the second harmonicbeam caused by the first pass. Similarly, the fourth pass can “undo” therelative divergence of the two beams caused by the third pass, etc.

[0119]FIGS. 1 and 2 also apply to the general case of a single nonlinearconversion process, of which SHG is one specific example. The nonlinearconversion process can be any one of SHG, SFG, DFG, OPA. To describe thegeneral case, in the above descriptions of FIGS. 1 and 2 detailing SHG,the references to the pump beam can be amended to refer to each inputbeam, and the references to the SHG beam can be amended to refer to eachadditional beam generated by the nonlinear conversion process. Becausein the general case, there are more than 2 beams, the ability to designthe optics to ensure collinearity of each additional and amplified beamgenerated on each pass may in some cases require more than one phasor.However, the generation or amplification on each pass for at least onesuch beam can be made collinear. The use of more than 1 phasor permitsone to achieve collinearity for a number of beams at least equal to thenumber of phasors.

[0120]FIG. 3 is a schematic top view of a double-pass,double-frequency-mixing apparatus 60, in accordance with the presentinvention, similar to FIG. 1 but with two simultaneous frequency mixingprocesses, and hence utilizing two phasors. To appreciate the operationof apparatus 60, it is helpful to consider the beam paths throughapparatus 60 before discussing the design of apparatus 60 in detail. Aset of input beams, which may comprise multiple frequencies, is receivedby face 10-2 of nonlinear medium 10, and is transmitted along beam path30 through nonlinear medium 10. Beams comprised of waves of at leastone, and in some cases multiple frequencies, according to the twofrequency relations of the two nonlinear frequency mixing processes, aregenerated within nonlinear medium 10, and are transmitted along beampath 30 through nonlinear medium 10. All of these beams are emitted fromface 10-1 of nonlinear medium 10, and are received by phasor 16. Thebeams are transmitted through phasor 16 and are received by phasor 26.The beams are transmitted through phasor 26 and are received by mirror18. The beams are reflected by mirror 18 and are received by mirror 20.The beams are reflected by mirror 20, reflected again from mirror 18,transmitted again through phasor 26 and phasor 16, and received by face10-1 of nonlinear medium 10. The beams are transmitted in a second passalong beam path 32 through nonlinear medium 10, and are emitted fromface 10-2 of nonlinear medium 10.

[0121] Beam paths 30 and 32 through nonlinear medium 10 are separatedfrom each other, similarly as indicated on FIG. 1b. This is accomplishedby choosing mirrors 18 and 20 such that they act as a first invertingtelescope to re-image reference plane 12 located at the center ofnonlinear medium 10 onto itself with negative unity magnification. Axis14, which is the axis of the telescope formed by mirrors 18 and 20, issubstantially centered within nonlinear medium 10 as shown in FIG. 1b.Thus, beam path 32 is the image of beam path 30 formed by the invertingtelescope, and separation of beam paths 30 and 32 is obtained byoffsetting beam path 30 from axis 14 as illustrated in FIG. 1b.Therefore, the two passes follow distinct paths through nonlinear medium10, where second pass beam path 32 is the inversion of first pass beampath 30 about axis 14. This separation of the second pass (beam path 32)from the first pass (beam path 30) is advantageous, since no additionaloptical elements are required to separate the second pass beams from thefirst pass beams.

[0122] A preferred method for coupling the output beams out of apparatus60 is to position an output turning mirror 44 within apparatus 60 sothat the second pass output beams following beam path 32 throughnonlinear medium 10 are reflected out of apparatus 60, and such thatoutput turning mirror 44 does not block the first pass input beamsfollowing beam path 30 through nonlinear medium 10.

[0123] The telescope in apparatus 60 (formed by mirrors 18 and 20) isdesigned as indicated in the discussion of FIG. 1a, i.e., with A=D=−1and C=0 at the phasor and designed to re-image reference plane 12 ontoitself with −1 magnification. This arrangement provides the advantagesof beam parallelism on both passes, and a degree of beam collinearityand astigmatism compensation, also as indicated above. Specifically, atleast as many collinearity conditions may be accommodated by design asthe number of phasors in the apparatus associated with each telescope.Even if a linearly varying phase shift is imposed on the beams bynonlinear medium 10 (e.g. if face 10-1 is not exactly perpendicular tothe beam axes), this variation is cancelled in double pass, and phasors16 and 26 will still simultaneously provide the required phase shiftbetween the first and second passes.

[0124]FIG. 4 is a schematic top view of a standing-wave singly-resonantoptical parametric oscillator (OPO) apparatus 70, configured inaccordance with the present invention. To appreciate the operation ofapparatus 70, it is helpful to consider the beam paths through apparatus70 before discussing the design of apparatus 70 in detail. A pump beamprovided by a pump source 42 is received by mirror 24. The pump beam istransmitted through mirror 24 to a face 10-2 of nonlinear medium 10, andis transmitted along a beam path 30 through nonlinear medium 10. Inaddition to the nonlinear materials previously described for use in anSHG apparatus, nonlinear materials that have been found to be useful inan OPO include AgGeSe₂, AgGaS₂ and ZnGeP₂. A signal beam and an idlerbeam, with frequencies which sum to the pump frequency, are generatedwithin nonlinear medium 10, and are also transmitted along beam path 30through nonlinear medium 10. The pump, signal, and idler beams areemitted from a face 10-1 of nonlinear medium 10, and are received by aphasor 16. The beams are transmitted through phasor 16 and are receivedby mirror 22. The pump and idler beams are transmitted through mirror 22along output path 38. A fraction of power of the signal beam may also betransmitted through mirror 22 along output path 38. The remainder of thesignal beam is retro-reflected by mirror 22 backward along path 30, andis transmitted again through phasor 16, and received by face 10-1 ofnonlinear medium 10. The signal beam is transmitted along beam path 30through nonlinear medium 10, and is emitted from face 10-2 of nonlinearmedium 10. The signal beam is received by a mirror 24 andretro-reflected by mirror 24 forward onto path 30, thus forming anoptical resonator for the signal beam.

[0125] The signal beam resonating in this optical resonator must have afrequency such that the round-trip optical path at the signal frequencyis an integer multiple of the signal free-space wavelength, (thefree-space speed of light divided by the frequency). Thus, the signalfrequency is restricted to a set of discrete frequencies, known as the“modes” of the optical resonator. Only the signal beam circulates in theoptical resonator, hence the OPO apparatus 70 is singly-resonant.

[0126] The purpose of phasor 16 is to adjust the total optical pathlength of the optical resonator, thus permitting the adjustment of thediscrete frequencies available to the signal beam. By adjusting thephasor such that the optical path of the resonator changes by a fullsignal wavelength, any frequency can be made available for the signalbeam. For example, consider a signal beam with wavelength substantiallyequal to 1550 nm. The refractive index of BK7 glass at 1.550 μm isn=1.50. Since the beam makes a double pass through phasor 16, a full1.550 μm wavelength adjustment of the optical path is obtained byvarying the phasor thickness seen by the signal beam by L_(λ)=0.7525 μm.Phasor 16 is preferably inserted into assembly 70 so that all beams areincident on phasor 16 at or near Brewster's angle and have ppolarization (i.e., electric field vector lying in the plane ofincidence of a phasor surface), to reduce reflection losses from thesurfaces of phasor 16. Alternatively, phasor 16 may have anantireflection coating on its optical surfaces so that the phasor can beused at angles other than Brewster's angle without introducingsubstantial reflection losses. Mirrors 22 and 24 form an opticalresonator for the signal beam. This resonator may be stable or unstable.A stable resonator requires that at least one of mirrors 22 or 24 beconcave, and that the radii of curvature of mirrors 22 and 24, and thediffractive path between them meet the stability criteria known by thoseskilled in the art. In prior art designs, the optical path of aresonator has been adjusted by translating one of mirrors 22 or 24parallel to path 30, to vary the physical length of the opticalresonator. Using a phasor is advantageous because translating a phasorwith a small wedge angle adjusts the optical path much more preciselythan translating one of mirrors 22 or 24, and the optical path of afixed phasor can be adjusted by one of the methods described previously.

[0127] Although the example in FIG. 4 is of a standing-wave OPO, it isevident to those skilled in the art of OPOs that the invention can alsobe applied to a traveling-wave OPO, which may consist of a ringresonator possessing mirrors in addition to 22 and 24, or which caninvolve manipulation of the polarization of the beams. Also, in asingly-resonant OPO, the pump beam may be substantially reflected byeither of mirrors 22 and 24, but not both, and the idler beam may besubstantially reflected by either of mirrors 22 and 24, but not both.This is so that substantially no power of either pump or idlercirculates inside the optical resonator.

[0128]FIG. 5a is a schematic top view of a standing-wave,doubly-resonant OPO apparatus 80, in accordance with the presentinvention. To appreciate the operation of apparatus 80, it is helpful toconsider the beam paths through apparatus 80 before discussing thedesign of apparatus 80 in detail. A pump beam provided by a pump source42 is received by mirror 24. The pump beam is transmitted through mirror24 to a face 10-2 of nonlinear medium 10, and is transmitted along apath 30 through nonlinear medium 10. A signal beam and an idler beam,with frequencies which sum to equal the pump frequency, are generatedwithin nonlinear medium 10, and are also transmitted along beam path 30through nonlinear medium 10. The pump, signal, and idler beams areemitted from a face 10-1 of nonlinear medium 10, and are received by aphasor 16. The beams are transmitted through phasor 16 and are receivedby a mirror 23. The pump beam is transmitted through mirror 23 alongoutput path 38. A fraction of the power of the signal and idler beamsmay also be transmitted through mirror 23 along output path 38. Theremainder of the signal and idler beams are retro-reflected by mirror 23backward along path 30, and are transmitted again through phasor 16, andreceived by face 10-1 of nonlinear medium 10. The signal and idler beamsare transmitted along beam path 30 through nonlinear medium 10, and areemitted from face 10-2 of nonlinear medium 10. The signal and idlerbeams are received by a mirror 24 and retro-reflected by mirror 24forward onto path 30, thus forming an optical resonator for both of thesignal and idler beams. Position transducer 25 permits the adjustment ofthe physical cavity length by translating mirror 23 parallel to path 30.Examples of position transducer 25 include a translation stage with amotor and a piezo-electric transducer (PZT).

[0129] Each of the signal and idler beams resonating in this opticalresonator must have a frequency such that the round-trip optical path atthe signal frequency is an integer multiple of the signal free-spacewavelength, and the round-trip optical path at the idler frequency is aninteger multiple of the idler free-space wavelength. Thus, both thesignal and idler frequencies are restricted to respective sets ofdiscrete frequencies, known as the “modes” of the optical resonator.Both of the signal and idler beams circulate in the optical resonator,hence the OPO apparatus 80 is doubly-resonant. These restrictionsconstitute two conditions for efficient operation of this OPO. A thirdcondition is that the sum of the frequencies of the signal and idlerbeams equals the pump frequency. Since the signal and idler frequenciesare the only two non-restricted parameters, the doubly-resonant OPO willnot operate efficiently under conditions of arbitrary optical pathlength and pump frequency. In the prior art, either the optical lengthof the resonator or the pump frequency would have to be adjusted so thatall three conditions could be attained simultaneously. Efficientoperation of a prior art OPO only occurred for discrete values of theresonator length (holding pump frequency fixed) or pump frequency(holding resonator length fixed), and the frequencies of the signal andidler beams could only be discrete values. Continuous tuning of thesignal and/or idler frequencies required adjusting both the resonatorlength and the pump frequency. The adjustment of phasor 16, incombination with translation of mirror 23, permits continuous andindependent adjustment of the optical path lengths of the signal andidler beams circulating in the optical resonator. In this manner, thesignal and idler frequencies may be tuned to arbitrary values (with thecondition that they sum to the pump frequency), while maintainingefficient operation of the OPO, without the need to adjust the pumpfrequency. They may even be tuned continuously by simultaneous andsynchronized adjustment of the phasor 16 and mirror 23.

[0130]FIG. 5b is a schematic top view of a standing-wave doubly-resonantOPO apparatus 90, in accordance with the present invention. Toappreciate the operation of apparatus 90, it is helpful to consider thebeam paths through apparatus 90 before discussing the design ofapparatus 90 in detail. A pump beam provided by a pump source 42 isreceived by mirror 24. The pump beam is transmitted through mirror 24 toa face 10-2 of nonlinear medium 10, and is transmitted along a beam path30 through nonlinear medium 10. A signal beam and an idler beam, withfrequencies which sum to the pump frequency, are generated withinnonlinear medium 10, and are also transmitted along beam path 30 throughnonlinear medium 10. The pump, signal, and idler beams are emitted fromface 10-1 of nonlinear medium 10, and are received by a phasor 16. Thebeams are transmitted through phasor 16 and are received by a phasor 26.The beams are transmitted through phasor 26 and are received by mirror22. The pump beam is transmitted through mirror 22 along output path 38.A fraction of power of the signal and idler beams may also betransmitted through mirror 22 along output path 38. The remainder of thesignal and idler beams are retro-reflected by mirror 22 backward alongpath 30, and are transmitted again through phasor 26 and phasor 16, andreceived by face 10-1 of nonlinear medium 10. The signal and idler beamsare transmitted along beam path 30 through nonlinear medium 10, and areemitted from face 10-2 of nonlinear medium 10. The signal and idlerbeams are received by a mirror 24 and retro-reflected by mirror 24forward onto path 30, thus forming an optical resonator for both of thesignal and idler beams.

[0131] As with apparatus 80 described in FIG. 5a, it is desirable inapparatus 90 to adjust the optical path lengths of the resonator for thesignal and idler beams independently, continuously, and synchronously.The independent adjustment is accomplished by adjusting phasors 16 and26, which are preferably chosen to have linearly independent materialdispersion at the signal and idler frequencies. By this choice,adjustment of one phasor changes the relative optical paths of thesignal and idler beams by a different amount than the other phasor. Aswith apparatus 80, synchronous and continuous adjustment of the phasorsin apparatus 90 provides continuous tuning of the signal and idlerfrequencies. Depending on the signal and idler, the phasors may need tobe adjusted at different rates to accomplish continuous tuning.

[0132]FIG. 5c is a schematic top view of a standing-wave doubly-resonantOPO apparatus 100, in accordance with the present invention. Toappreciate the operation of apparatus 100, it is helpful to consider thebeam paths through apparatus 100 before discussing the design ofapparatus 100 in detail. A pump beam provided by a pump source 42 isreceived by mirror 24. The pump beam is transmitted through mirror 24 toa face 10-2 of nonlinear medium 10, and is transmitted along a beam path30 through nonlinear medium 10. A signal beam and an idler beam, withfrequencies which sum to the pump frequency, are generated withinnonlinear medium 10, and are also transmitted along beam path 30 throughnonlinear medium 10. The pump, signal, and idler beams are emitted fromface 10-1 of nonlinear medium 10, and are received by a composite phasor36. The beams are transmitted through phasor 36 and are received by amirror 22. The pump beam is transmitted through mirror 22 along outputpath 38. A fraction of the power of the signal and idler beams may alsobe transmitted through mirror 22 along output path 38. The remainder ofthe signal and idler beams are retro-reflected by mirror 22 backwardalong path 30, and are transmitted again through phasor 36, and receivedby face 10-1 of nonlinear medium 10. The signal and idler beams aretransmitted along beam path 30 through nonlinear medium 10, and areemitted from face 10-2 of nonlinear medium 10. The signal and idlerbeams are received by a mirror 24 and retro-reflected by mirror 24forward onto path 30, thus forming an optical resonator for both of thesignal and idler beams.

[0133] Similarly to apparatus 80, it is advantageous in apparatus 100 toadjust the optical path lengths of the resonator for the signal andidler beams synchronously so that the optical path length of the signalbeam increases as the optical path length of the idler beam decreases,changing the signal and idler discrete mode frequencies oppositely andby the same amount. In this manner, the signal and idler frequencies maybe tuned continuously without adjusting either the resonator physicallength or the pump frequency. The composite phasor 36 accomplishes thissynchronous adjustment of optical path lengths by design. Phasor 36 issimilar to the combination of phasors 16 and 26 in apparatus 90, but inaddition the two phasors 16 and 26 should preferably be designed to beadjusted at the same rate to maintain synchronism, and attached togetherin series to form composite phasor 36. The adjustment of phasor 36 maybe by translation, or by any of the other adjustment modes describedpreviously.

[0134] Although the examples in FIGS. 5 are of standing-wave OPOs, it isevident to those skilled in the art of OPOs that the invention can alsobe applied to traveling-wave OPOs, which may consist of ring resonatorspossessing mirrors in addition to 22 (or 23) and 24, or whichalternatively may involve manipulation of the polarization of the beams.In addition, in a doubly-resonant OPO, the pump beam may besubstantially reflected by either of mirrors 22 or 23 and 24, but notboth, so that substantially no power of the pump circulates inside theoptical resonator.

[0135]FIGS. 5a, 5 b, and 5 c also illustrate examples of pump-enhancedsingly-resonant OPOs in accordance with the present invention. In apump-enhanced singly-resonant OPO, both the pump beam and signal beamcirculate within the optical resonator. The optical path of theresonator at the pump wavelength must equal substantially an integernumber of pump wavelengths so that the pump beam may efficiently coupleinto the resonator. To tune the signal wavelength while maintaining afixed pump wavelength, two adjustments must be made substantiallysimultaneously, so as to change the optical path of the resonator at thesignal wavelength, while keeping it fixed at the pump wavelength. Suchadjustments are the same as those described previously for FIGS. 5a-5 c,including one phasor and the physical cavity length, two independentphasors, or a composite phasor which, by design, provides bothadjustments synchronously. Similarly, the pump wavelength may be tunedwhile the signal wavelength is fixed; the pump wavelength and signalwavelength may each be tuned independently (FIGS. 5a and 5 b), or atrates in a fixed ratio (FIGS. 5a, 5 b, and 5 c).

[0136]FIG. 6 is a schematic top view of a standing-wave, pump-enhanceddoubly-resonant OPO (sometimes called a triply-resonant OPO) apparatus110, in accordance with the present invention. To appreciate theoperation of apparatus 110, it is helpful to consider the beam pathsthrough apparatus 110 before discussing the design of apparatus 110 indetail. A pump beam, provided by a pump source 42, is received by mirror24. The pump beam is transmitted through mirror 24 and is received by acomposite phasor 46′. The pump beam is then transmitted through phasor46′ to a face 10-2 of nonlinear medium 10, and is transmitted along abeam path 30 through nonlinear medium 10. A signal beam and an idlerbeam, with frequencies which sum to the pump frequency, are generatedwithin nonlinear medium 10, and are also transmitted along beam path 30through nonlinear medium 10. The pump, signal, and idler beams areemitted from face 10-1 of nonlinear medium 10, and are received bycomposite phasor 46. The beams are transmitted through phasor 46 and arereceived by a mirror 22. A fraction of the power of each beam may betransmitted through mirror 22 along output path 38. The remainder ofeach beam is retro-reflected by mirror 22 backward along path 30, and istransmitted again through phasor 46, and received by face 10-1 ofnonlinear medium 10. The pump, signal, and idler beams are transmittedalong beam path 30 through nonlinear medium 10, and are emitted fromface 10-2 of nonlinear medium 10. The pump, signal, and idler beams arereceived by composite phasor 46′. The beams are transmitted throughphasor 46′ and are received by mirror 24 and retro-reflected by mirror24 forward onto path 30, thus forming an optical resonator for all threebeams.

[0137] Similarly to apparatus 100 of FIG. 5c, it is advantageous inapparatus 110 to adjust the optical path lengths of the resonator forall three beams synchronously so that the optical path lengths of eachbeam change by an amount appropriate for the type of wavelength tuningdesired. One such type of tuning involves a fixed pump wavelength andoppositely varying signal and idler wavelengths, as described forapparatus 100. The phasors 46 and 46′ may be designed such thatadjustment of each phasor varies the optical path lengths at the signaland idler wavelengths oppositely and in the correct ratio while notchanging the optical path at the pump wavelength. Another type of tuninginvolves variable pump and idler wavelengths and a fixed signalwavelength. The phasors 46 and 46′ may advantageously be designed suchthat their adjustments vary the optical paths of the pump and idlerwavelengths in the appropriate ratio while not changing the optical pathat the signal wavelength. Yet another type of tuning involves fixedratios of tuning rates among all three waves. Thus, the pump, signal,and idler frequencies may be tuned continuously without adjusting theresonator physical length. The composite phasors 46 and 46′ accomplishthis synchronous adjustment of optical path lengths. Phasors 46 and 46′are similar to phasor 36 in apparatus 100, but are combinations of threephasors instead of two. The adjustments of phasors 46 and 46′ may be bytranslation, or by any of the other adjustment modes describedpreviously. Although only one composite phasor is required to obtainsynchronous tuning of the three beams, an additional phasor on theopposite side of the nonlinear medium 10 is advantageous to maintainproper phase-matching on both the forward and backward passes throughnonlinear medium 10 in a standing-wave OPO. Alternatively to the phasor46′, mirror 24 may be designed to impart an additional relative phase tothe three beams such that they have the appropriate relative phase uponentry into nonlinear medium 10 at face 10-2. Mirror 24 may be coateddirectly onto face 10-2, in which case it preferably imparts zeroadditional relative phase to the three beams. In a ring OPO, only onephasor 46 is required because a ring OPO has no backward pass throughthe nonlinear medium 10.

[0138] A triply-resonant OPO in accordance with the present inventionmay be created by the addition of another phasor to any of FIGS. 5a, 5b, or 5 c, and the optional duplication of the set of phasors (andcavity length adjustment) to the opposite side of nonlinear medium 10.The additional degree of freedom accorded by adjustment of this phasorpermits tuning of any combination of all three beams, and themaintenance of the resonance of all three beams in the opticalresonator, similarly to the conditions and limitations described foreach of FIGS. 5a, 5 b, and 5 c.

[0139] It is also evident to those skilled in the art of OPOs andnonlinear optics that a multipass apparatus similar to that shown inFIG. 1 may be combined with any of the OPO designs shown in FIGS. 4, 5,or 6.

[0140] The advantageous phase adjustment provided by a wedged phasor canbe obtained in embodiments of the present invention which do not includean inverting telescope. Multipass embodiments of the invention can haveany number of passes greater than or equal to two.

[0141] The foregoing detailed description of the invention includespassages that are chiefly or exclusively concerned with particular partsor aspects of the invention. It is to be understood that this is forclarity and convenience, that a particular feature may be relevant inmore than just the passage in which it is disclosed, and that thedisclosure herein includes all the appropriate combinations ofinformation found in the different passages. Similarly, although thevarious figures and descriptions herein relate to specific embodimentsof the invention, it is to be understood that where a specific featureis disclosed in the context of a particular figure or embodiment, suchfeature can also be used, to the extent appropriate, in the context ofanother figure or embodiment, in combination with another feature, or inthe invention in general.

[0142] Further, while the present invention has been particularlydescribed in terms of certain preferred embodiments, the invention isnot limited to such preferred embodiments. Rather, the scope of theinvention is defined by the appended claims.

What is claimed is:
 1. Apparatus for the nonlinear frequency conversionof optical radiation, the apparatus comprising: a) an opticallynonlinear medium that receives at least one input beam wherein each ofsaid at least one beam makes N passes through the nonlinear medium,where N is an integer ≧2, to thereby generate at least one additionalbeam wherein the sum of the input and additional beams is M, wherein${\sum\limits_{i = 1}^{M}{S_{i}\omega_{i}}} = 0$

for each nonlinear frequency conversion process, wherein i denotes aparticular beam of the M beams, ω_(i) denotes the frequency of a beam i,wherein S_(i) is +1, 0 or −1; and b) a telescope subassembly having anABCD matrix with matrix coefficients substantially A=−1, B has any realvalue, substantially C=0 and substantially D=−1, for receiving andcoupling the input and additional beams emitted from the nonlinearmedium after a pass number J, back into the medium for a pass numberJ+1, where 1≦J<N, and wherein the additional beam issues from thenonlinear medium after pass number J+1.
 2. Apparatus forfrequency-doubling optical radiation, the apparatus comprising: a) anoptically nonlinear medium that receives a first beam of opticalradiation having a first frequency, wherein the first beam makes Npasses through the nonlinear medium, where N is an integer ≧2, tothereby generate a second beam having a second frequency substantiallyequal to twice the first frequency; and b) a wedged phasor for receivingand adjusting a relative phase of the first and second beams before apass number K of the beams through the nonlinear medium, where 2≦K≦N. 3.Apparatus for frequency-doubling optical radiation, the apparatuscomprising: a) an optically nonlinear medium that receives a first beamof optical radiation having a first frequency, wherein the first beammakes N passes through the nonlinear medium between a first face and asecond face of the medium, where N is an integer ≧2, to thereby generatea second beam having a second frequency substantially equal to twice thefirst frequency; b) a first telescope subassembly having a first ABCDmatrix with matrix coefficients substantially A=−1, B has any realvalue, substantially C=0 and substantially D=−1, for receiving andcoupling the first and second beams, emitted from the medium after apass number J, back into the nonlinear medium for a pass number J+1,where 1≦J≦N wherein the second beam issues from the nonlinear mediumafter pass number J+1; and c) a wedged phasor for receiving andadjusting a relative phase of the first and second beams before a passnumber K of the beams though the medium, where 2≦K≦N, where the phasoris positioned between the nonlinear medium and the telescopesubassembly.
 4. The apparatus of claim 3, wherein a reference planewithin said nonlinear medium is substantially re-imaged onto itself withnegative unity magnification by said telescope subassembly, and whereinthe reference plane is substantially perpendicular to a direction ofpropagation of said first and second beams.
 5. The apparatus of claim 4,wherein said first beam is substantially a Gaussian beam having a beamwaist with a 1/natural log e amplitude radius w that is related to adistance L between said first and second faces according toL_(opt)/3<L<3 L_(opt), where L_(opt)=5.687πw²n_(ω)/λ, n_(ω) is an indexof refraction of said nonlinear medium at said first frequency, and λ isa free space wavelength of said first beam, and wherein the beam waistis substantially located on said reference plane and said referenceplane is substantially centered between said first and second faces. 6.The apparatus of claim 5, wherein said distance L is substantially equalto L_(opt).
 7. The apparatus of claim 3, wherein said nonlinear mediumis birefringently phase-matched.
 8. The apparatus of claim 3, whereinsaid nonlinear medium is quasi-phase-matched.
 9. The apparatus of claim8, wherein said nonlinear medium comprises periodically-poled PotassiumTitanyl Phosphate (KTiOPO₄), periodically-poled Lithium Niobate(LiNbO₃), or periodically-poled Lithium Tantalate (LiTa O₃).
 10. Theapparatus of claim 3, wherein said first and second beams pass throughsaid wedged phasor at an angle substantially equal to Brewster's angleand wherein said beams are incident on a face of said wedged phasor withsubstantially p polarization.
 11. The apparatus of claim 3, wherein saidnonlinear medium is substantially a parallelepiped having a center lineintersecting centers of said first and second medium faces, theapparatus further comprising a second telescope subassembly having asecond ABCD matrix with matrix coefficients substantially A=−1, B hasany real value, substantially C=0 and substantially D=−1, wherein saidfirst telescope subassembly has a first axis which is substantiallycollinear with the center line, wherein the second telescope subassemblyhas a second axis which is parallel to and spaced apart from the centerline, and wherein a plane containing the first axis and the second axisis substantially parallel to a face of the parallelepiped.
 12. Theapparatus of claim 3, further comprising means for astigmatismcompensation for at least one of said first telescope subassembly andsaid phasor.
 13. The apparatus of claim 3, further comprising means forensuring collinearity of said second beam with said first beam for atleast one of said passes through said nonlinear medium.
 14. A method forfrequency-doubling optical radiation, the method comprising: a)transmitting a first beam of optical radiation having a first frequencyω₁ through an optically nonlinear medium so that the first beam makes Npasses through the nonlinear medium, where N is an integer ≧2, tothereby generate a second beam having a second frequency ω₂substantially equal to twice the first frequency; and b) passing thefirst and second beams, emitted from the medium after a pass number J,through a telescope subassembly having an ABCD matrix with matrixcoefficients substantially A=−1, B has any real value, substantially C=0and substantially D=−1, whereby the first and second beams are coupledback into the medium for a pass number J+1, where 1≦J<N and wherein thesecond beam issues from the nonlinear medium after pass number J+1. 15.A method for frequency-doubling optical radiation, the methodcomprising: a) transmitting a first beam of optical radiation having afirst frequency ω₁ through an optically nonlinear medium so that thefirst beam makes N passes through the nonlinear medium, where N is aninteger ≧2, to thereby generate a second beam having a second frequencyω₂ substantially equal to twice the first frequency; and b) passing thefirst and second beams through a wedged phasor for adjusting a relativephase of the first and second beams before a pass number K of the beamsthrough the nonlinear medium, where 2≦K≦N.
 16. A method forfrequency-doubling optical radiation, the method comprising: a)transmitting a first beam of optical radiation having a first frequencyω₁ through an optically nonlinear medium so that the first beam makes Npasses through the nonlinear medium between a first face and a secondface of the medium, where N is an integer ≧2, to thereby generate asecond beam having a second frequency ω₂ substantially equal to twicethe first frequency; b) passing the first and second beams, emitted fromthe medium after a pass number J, through a first telescope subassemblyhaving a first ABCD matrix with matrix coefficients substantially A=−1,B has any real value, substantially C=0 and substantially D=−1, wherebythe first and second beams are coupled back into the medium for a passnumber J+1, where 1≦J<N; and c) passing the first and second beamsthrough a wedged phasor for adjusting a relative phase of the first andsecond beams before a pass number K of the beams through the nonlinearmedium, where 2≦K≦N, where the phasor is positioned between thenonlinear medium and the telescope subassembly where the second beamissues from the nonlinear medium after pass number J+1.
 17. The methodof claim 16, wherein a reference plane within the nonlinear medium issubstantially re-imaged onto itself with negative unity magnification bysaid telescope subassembly, and wherein the reference plane issubstantially perpendicular to a direction of propagation of said firstand second beams.
 18. The method of claim 17, wherein said first beam issubstantially a Gaussian beam having a beam waist with a 1/natural log eamplitude radius w that is related to a distance L between said firstand second faces according to L_(opt)/3<L<3 L_(opt), whereL_(opt)=5.68πw²n_(ω)/λ, n_(ω) is an index of refraction of saidnonlinear medium at said first frequency, and λ is a free spacewavelength of said first beam, and wherein the beam waist issubstantially located on said reference plane.
 19. The method of claim18, wherein said distance L is substantially equal to L_(opt).
 20. Themethod of claim 16, wherein said nonlinear medium is birefringentlyphase-matched.
 21. The method of claim 16, wherein said nonlinear mediumis quasi-phase-matched.
 22. The method of claim 21, wherein saidnonlinear medium comprises periodically-poled Potassium TitanylPhosphate (KTiOPO₄), periodically-poled Lithium Niobate (LiNbO₃) orperiodically-poled Lithium Tantalate (LiTaO₃).
 23. The method of claim16, wherein said first and second beams pass through said wedged phasorat an angle substantially equal to Brewster's angle and wherein saidbeams are incident on a face of said wedged phasor with substantially ppolarization.
 24. The method of claim 16, wherein said nonlinear mediumis substantially a parallelepiped having a center line intersectingcenters of said first and second medium faces, the method furthercomprising passing said first and second beams through a secondtelescope subassembly having a second ABCD matrix with matrixcoefficients substantially A=−1, B has any real value, substantially C=0and substantially D=−1, wherein said first telescope subassembly has afirst axis which is substantially collinear with the center line,wherein the second telescope subassembly has a second axis which isparallel to and spaced apart from the center line, and wherein a planecontaining the first axis and the second axis is substantially parallelto a face of the parallelepiped.
 25. The method of claim 16, furthercomprising compensating for the astigmatism of at least one of saidtelescope subassembly and said phasor.
 26. The method of claim 16,further comprising ensuring collinearity of said second beam with saidfirst beam for at least one of said passes through said nonlinearmedium.
 27. An OPO apparatus comprising: a) a source of opticalradiation; b) an optically nonlinear medium that receives a pump beam ofoptical radiation having a first frequency ω₃, to thereby generate asignal beam having a frequency ω₁, and an idler beam having a frequencyω₂ such that ω₁+ω₂=ω₃; c) a resonant optical cavity containing thenonlinear medium in which cavity at least the signal beam resonates d)at least one phasor for receiving and adjusting the phase of theresonating beam or beams.
 28. The apparatus of claim 27, wherein saidfirst beam is substantially a Gaussian beam having a beam waist with a1/natural log e amplitude radius w that is related to a distance Lbetween said first and second faces according to L_(opt)/3<L<3 L_(opt),where L_(opt)=5.68πw²n₃/λ₃, n₃ is the index of refraction of saidnonlinear medium at said first frequency, and λ₃ is the free spacewavelength of said pump beam, and wherein the pump beam waist issubstantially located on said reference plane and said reference planeis substantially centered between said first and second faces.
 29. Theapparatus of claim 28, wherein said distance L is substantially equal toL_(opt).
 30. The apparatus of claim 27, wherein said nonlinear medium isbirefringently phase-matched.
 31. The apparatus of claim 27, whereinsaid nonlinear medium is quasi-phase-matched.
 32. The apparatus of claim31, wherein said nonlinear medium comprises periodically-poled PotassiumTitanyl Phosphate (KTiOPO₄), periodically-poled Lithium Niobate(LiNbO₃), or periodically-poled Lithium Tantalate (LiTaO₃).
 33. Theapparatus of claim 27, wherein resonating beams pass through said wedgedphasor at an angle substantially equal to Brewster's angle and whereinresonating beams are incident on a face of said wedged phasor withsubstantially p polarization.
 34. The apparatus of claim 27, furthercomprising means for astigmatism compensation for at least one of saidtelescope subassemblies and said phasor.
 35. The apparatus of claim 27wherein said OPO is a singly or doubly resonant OPO.
 36. The apparatusof claim 27 wherein said pump beam is enhanced by said resonant opticalcavity.
 37. The apparatus of claim 27 wherein said pump beam, said idlerbeam and said signal beam are all collinear.
 38. The apparatus of claim27 wherein said at least one phasor comprises a composite structurecomprising at least two materials of different optical dispersion 39.The apparatus of claim 27 wherein said at least one phasor isbirefringent.
 40. The apparatus of claim 27 wherein said phasorcomprises optical glass, KTP, LiNbO₃ or fused silica.
 41. The apparatusof claim 27 wherein the refractive index of said phasor is adjustable.42. The apparatus of claim 27 wherein said OPO is triply resonant. 43.The apparatus of claim 27 wherein said phasor is a wedged phasor. 44.The apparatus of claim 27 wherein said nonlinear material comprisesAgGeSe₂, AgGaS₂, or ZnGeP₂.
 45. A method for frequency conversion ofoptical radiation using an OPO, the method comprising: a) transmitting afirst beam of optical radiation having a first frequency ω₃ through anoptically nonlinear medium contained within a resonant optical cavity tothereby generate a signal beam having a frequency ω₁ and an idler beamhaving a frequency ω₂ such that ω₁+ω₂=ω₃; b) causing at least the signalbeam to resonate within said optical cavity; c) passing said signal beamthrough at least one phasor and adjusting the refractive index of saidat least one phasor to thereby alter the phase of said signal beam. 46.The method of claim 45, wherein said first beam is substantially aGaussian beam having a beam waist with a 1/natural log e amplituderadius w that is related to a distance L between said first and secondfaces according to L_(opt)/3<L<3 L_(opt), where L_(opt)=5.68πw²n₃/λ₃, n₃is an index of refraction of said nonlinear medium at said firstfrequency, and λ₃ is a free space wavelength of said first beam, andwherein the beam waist is substantially located on said reference plane.47. The method of claim 46, wherein said distance L is substantiallyequal to L_(opt).
 48. The method of claim 45, wherein said nonlinearmedium is birefringently phase-matched.
 49. The method of claim 45,wherein said nonlinear medium is quasi-phase-matched.
 50. The method ofclaim 45, wherein said nonlinear medium comprises periodically-poledKTiOPO₄.
 51. The method of claim 45, wherein said phasor is a wedgedphasor and said first beam passes through said wedged phasor at an anglesubstantially equal to Brewster's angle and wherein said first beam isincident on a face of said wedged phasor with substantially ppolarization.